We propose to evaluate the optimal moment for catheterization in patients presenting with acute coronary syndromes by comparing rapid catheterization on the day of admission (within 8 hours of admission, with an average time close to 3 hours, as in the rapid strategy arm of the ISAR-COOL trial) with a slower approach where the examination is scheduled for the next working day (8 to 60 hours post admission, with an average close to 24 hours). Patients included will present with severe unstable angina defined as a TIMI score > 3 All patients must present with an indication for catheterization and they will receive the same optimal pharmacological treatment including abciximab (ReoPro*) when undergoing PCI and started just before the procedure as indicated in the label of the drug (substitution by another drug of the class, eptifibatide or tirofiban, is not possible in the catheterization laboratory according to the labels of these two other drugs). Randomization will evaluate only time to catheterization: rapidly, as soon as possible following admission (within 8 hours of admission) versus a delayed approach (8 to 60 hours following admission). The goal of randomization is to determine the ideal time to catheterization while indications for catheterization, pharmacological treatment, and patient care remain constant. This is a pragmatic study aiming to compare 2 different strategies in the management of ACS.